Scheduling

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Chapter 16
Scheduling of
Operations

Scheduling of Operations

A planning tool for the short term
 Provides an opportunity to make use of
new information as we approach real time
 A methodology to fine tune planning and
decision making due to the occurrence of
random events
 Enables organisations to focus on microresources, a single machine, a set of
workers and so on. Such a focus is neither
possible nor warranted at the medium or
long term planning.
Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Planning Context in the short term
 How do we assign the jobs to various work
centers?
 Within each work center, how do we rank
order the jobs?
 How do we assign other resources such as
skilled workers and material handling
devices to the operating system?
 How do we react to a breakdown in the
system?
 How do we measure the performance of the
operating system?
Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Scheduling

Alternative Terminologies
 Loading is defined as a planning methodology using
which the resources in an operating system are assigned
with adequate number of jobs during the planning
horizon (of say a week)
 Scheduling is defined as the process of rank ordering the
jobs in front of each resource with a view to maximise
some chosen performance measure
 Routing is defined as the order in which the resources
available in a shop are used by the job for processing
 Sequencing is the ordering of operations of the jobs in
the operating system
 Dispatching is defined as the administrative process of
authorising processing of jobs by resources in the
operating system as identified by the scheduling system
Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Scheduling Context
 Number of jobs (n)
 Number of machines (m)
 Shop configuration
 Flow shop
 Job Shop
 Cellular Manufacturing System
 Job priorities
 FCFS, SPT, LPT, EDD, LS, Random
 Performance Measures
 Due date based: lateness, tardiness
 Completion based: Flow time, make span
 Inventory/cost based
Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Pure Flow Shop

A graphical illustration
Job 1
Job 2
Job n

Machine
1

Machine
2

Machine
3

...

Machine
m

• In a flow shop, the resources are organised one
after the other in the order the jobs are
processed
• A pure flow shop is one in which all the jobs visit
all the machines in the same order (beginning at
machine 1 and ending at machine m)
• In a mixed flow shop, some jobs are allowed to
skip machines in between
Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Job Shop

A graphical illustration
Machine
1

Machine
3

Job 1: 1-4-2-5-6
Job 2: 3-2-1-4-6-7
Job 3: 2-3-4-7-5-6
Machine
6

Job 1

Job 3

...

Machine
4

Machine
7

Machine
2
Machine
5

Job 2

In a job shop, machines are not organised in any processing
order. Rather similar type of resources is grouped together
Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Scheduling Rules
A sample

Shortest processing time (SPT): Chooses the job with the least
processing time among the competing list and schedules it ahead
of the others
Longest processing time (LPT): The job with the longest
processing time is scheduled ahead of other competing jobs
Earliest Due Date (EDD): Establishes priorities on the basis of the
due date for the jobs.
Critical Ratio (CR): Critical ratio estimates the criticality of the job
by computing a simple ratio using processing time information and
due date. A smaller value of CR indicates that the job is more
critical.

Critical Ratio (CR ) 

Re maining time
( Due Date  Current Date )

Re maining Work Re maining Pr oces sin g Time

First Cum First Served (FCFS): Schedules jobs simply in their
order of job arrival
Random Order (RAN): Assign priorities to jobs on a random basis.
Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Scheduling Rules

An illustration of their application
Current time = 0
Job No.

Processing
time (mins)

Order of
arrival

Due by

CR

Random
Number

1

12

1

23

1.92

0.233

2

9

2

24

2.67

0.857

3

22

3

30

1.36

0.518

4

11

4

20

1.82

0.951

Rule

Rank ordering of jobs based on

SPT

2–4–1–3

LPT

3–1–4–2

EDD

4–2–1–3

CR

3–4–1–2

FCFS

1–2–3–4

RAN

1–3–2–4

Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Performance Criterion
Completion based measures

 Flow time is defined as the elapsed time
between releasing a job into the shop and the
time of completion of processing of the job
Release time of the job
Completion time of the job
Flow time of the job

: Ri
: Ci
: Fi = (Ri – Ci)

 Make span is defined as the time taken to
complete all the jobs released into the shop for
processing
Make span (Max. Completion time):C max  max{Ci }
i

Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Performance Criterion
Due date based measures

 Lateness defined as the difference between
completion time and due date.
If the due date for a job i is denoted as Di, then
Lateness of the job: Li = (Ci – Di)

 If a job is completed ahead of time, instead
of computing a negative value for Li if we
take zero, then the resulting measure is
known as tardiness
Tardiness of the job: Ti = max(0, Li)

Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Performance of Scheduling Rules
Example 16.2: An illustration (SPT)
Scheduling Rule: SPT
Processing
order

Release Completion
time (Ri)
time (Ci)

Flow
time (Fi)

Lateness

Tardiness

2

0

6

6

0

0

3

0

13

13

4

4

1

0

2

2

-17

0

4

0

21

21

4

4

Mean

10.50

10.50

-2.25

2.00

Maximum

21.00

21.00

4.00

4.00

Minimum

2.00

2.00

-17.00

0.00

No. of tardy jobs = 2; Make span = 21

Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Performance of Scheduling Rules
Example 16.2: An illustration (EDD)
Scheduling Rule: EDD
Processing
order

Release Completion
time (Ri)
time (Ci)

Flow
time (Fi)

Lateness

Tardiness

1

0

4

4

-2

0

2

0

11

11

2

2

4

0

21

21

2

2

3

0

19

19

2

2

Mean

13.75

13.75

1.00

1.50

Maximum

21.00

21.00

2.00

2.00

Minimum

4.00

4.00

-2.00

0.00

No. of tardy jobs = 3; Make span = 21

Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Scheduling of Flow Shops
Johnson’s Rule

Step 1: Let t1i denote the processing time of job i in machine
1 and t2i denote the processing time in machine 2.
Step 2: Identify the job with the least processing time in the
list. If there are ties, break the tie arbitrarily.
a) If the least processing time is for machine 1, place
the job at the front of the sequence immediately after
any jobs already scheduled
b) If the least processing time is for machine 2, place
the job at the back of the sequence immediately
before any jobs already scheduled
c) Remove job i from the list.

Step 3. If there are no more jobs to be scheduled go to step
4. Otherwise go to step 1.
Step 4. The resulting sequence of jobs is the best schedule
to minimise the make span of the jobs.
Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Johnson’s Rule

An illustration: Example 16.3
Processing time

Job No

Machine 1

Machine 2

1

4

7

2

6

3

3

2

3

4

7

7

5

8

6

Job 3

Machine 1

3

3

Machine 2
1

2

1

1

1

3

3

3

3

4

5

1

6

Job 1

Job 4

Job 5

4

4

4

4

4

4

4

5

5

5

5

5

5

5

1

1

1

1

1

1

1

4

4

4

4

4

4

4

7

8

Job 2

5

2

2

2

2

2

2

5

5

5

5

5

5

2

2

2

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Time units
Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Job Shop Scheduling

An illustration (Example 16.4, SPT rule)

Machines 1 and 2 are assigned jobs 4 and 1 respectively using the SPT rule

Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Job Shop Scheduling

An illustration (Example 16.4, SPT rule)
After completion of
job 1, job 3 is
scheduled in machine
2 using SPT rule

Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Job Shop Scheduling

An illustration (Example 16.4, SPT rule)

Gantt Chart representation of the final schedule using the SPT rule

Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Job Shop Scheduling

An illustration (Example 16.4, EDD rule)

Gantt Chart representation of the final schedule using the EDD rule
Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Job Shop Scheduling

Performance Summary of SPT & EDD
Job No
1
2
3
4
Average

Due
10
12
9
14

SPT
Ci
13
21
17
18
17.25

Lateness
3
9
8
4
6.00

EDD
Ci
23
20
14
23
20.00

Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Lateness
13
8
5
9
8.75

Input – Output Control
A schematic illustration
Pending
Orders

Input rate
control

Existing
Load
Output rate
control

CONWIP

Completed
Orders

Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Operational Control Issues
Mass Production Systems

 Much of control and scheduling boils down
to appropriately arriving at balanced flow
of components in the shop floor
Design the system for balanced flow using Line
Balancing Techniques
 Given a certain availability of resources modify
the cycle time to meet daily production targets
 Machine Redeployment
 Altering Operator Allocations
 Adjusting Material Feed rates


 TAKT time provides a rhythm for the
overall functioning of the shop
Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Worker deployment for
adjusted TAKT: An illustration
Required output per day

400

450

371

2

2

2

Required output per shift
Net available production time
(Mins)

200

225

185.5

420

420

420

TAKT Time (Seconds)

126

112

136

1,764

1,764

1,764

14

16

13

28

32

26

No. of shifts per day

Work Content (Seconds)
No. of Operators required per
shift
Total number of operators
required

Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Theory of Constraints &
Synchronous Manufacturing
 Theory of constraints is a systematic body of
knowledge, which recognizes that
 Resources in manufacturing organizations differ from
one another in their ability to process components
 Statistical fluctuations and dependant events are
characteristic of resources in a manufacturing
organization
 Uses specific methods to improve the performance of
the system under these conditions.
 Synchronous manufacturing is a specific application of
theory of constraints to scheduling and operational
control of manufacturing systems
 In synchronous manufacturing the focus is on
synchronizing flow rather than balancing capacities
Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Theory of constraints
Guiding principles

 Do not balance capacity – balance flow
 The level of utilisation of a non-bottleneck
resource is determined by not by its own
potential but by some other constraints in the
system
 An hour lost at the bottleneck is an hour lost
at the entire system
 An hour saved at a non-bottleneck is a
mirage
 Bottlenecks govern both the throughput and
inventory in the system
Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Synchronous Manufacturing
The analogy of marching soldiers

Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

A comparison of marching
soldier & a production system
Resource

Marching Soldiers

Production System

Processing

Ground to be covered

Raw Material to be processed

WIP

Gap between the first and
the last soldier

Work in Process in the shop
floor

Throughput

The extent of ground
covered by the marching
soldiers
Amount of energy
expounded by the soldiers
to complete the march

Amount produced and sold by
the production system

Operating
Expenses

Objective

Cost of transforming the raw
material into throughput

To cover a certain extent of To achieve a certain
the ground in a given time throughput in a given time

Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Two types of resources
 Based on the capacity availability to meet demand
 Bottleneck resource
 Non-bottleneck resource
 bottleneck resources determine the (planned) output of the
system
 Ability to become a bottleneck if poorly scheduled
 Capacity constrained resource (CCR)
 Non-CCR
 CCR will ensure that the actual throughput do not deviate
from the planned in a manufacturing system.
Focusing on maximizing utilisation of bottleneck resource is key to maximising
throughput in a manufacturing system. On the other hand, scheduling is done in
synchronous manufacturing with reference to CCRs.
Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Synchronous Manufacturing
Guiding Principles

1 Do not focus on balancing capacities. Instead, focus on
synchronizing the flow
2 The marginal value of time spent at a bottleneck resource is
negligible. Do not attempt to reduce time at a non-bottleneck
resource.
2a. An hour gained at a non-bottleneck resource is a mirage
2b. An hour lost at a bottleneck resource is an hour of throughput loss

3 The level of utilization of a non-bottleneck resource is controlled
by other constraints within the system
4 Resources in the system must be utilized, not simply activated.
5 A constraint is any element that preempts the system from
achieving the goal of making more money.
6 The transfer time need not, and many time should not equal to
the process batch
Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Synchronous Manufacturing
Drum – Buffer – Rope Methodology

 Develop a schedule so that it is consistent with the
constraints of the systems (Drum)
 The schedule is actually the drum beat
 Protect the throughput of the system from statistical
fluctuations through the use of buffers at some critical
points in the system (Buffer)
 Tie the production at each resource to the drum beat
(Rope)

Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Constraint Management
In the Long run

Soft Constraints

Identify the
constraint
Hard constraints

Gainfully exploit it using
Synchronous Manufacturing

Mount a time bound
procedure for
removing the constraint

Constraints
shift elsewhere

Revised
systems

Progressive
Mind-set

Process
improvements

Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Scheduling of Operations
Chapter Highlights

 The focus shifts from operations planning to
operational control in the case of a short-term.
Scheduling aids operational control in
manufacturing and service systems.
 The scheduling context relates to the number of
jobs and machines in the system and the physical
configuration of the machines. These factors greatly
influence the complexity of scheduling.
 Flow shop and Job shops are two alternatives for
configuration of a manufacturing system. The
scheduling methodology and complexity differ
vastly between these two. Job shops are far more
complex to schedule than flow shops.
Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

Scheduling of Operations
Chapter Highlights…

 Johnson’s algorithm provides an optimal schedule for a
two machine – n job problem using the shortest
processing time rule for scheduling.
 Operational control in mass production systems are
primarily achieved through use of TAKT time based
scheduling.
 Theory of constraints indicates that scheduling of
operations must take into account the existence of
bottlenecks and statistical fluctuations in operations.
 Synchronous manufacturing principles apply the theory
of constraints and develop alternative schedules using a
drum – buffer – rope methodology.

Mahadevan (2010), “Operations Management: Theory & Practice”, 2nd Edition © Pearson Education

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